Question: Reduce to lowest terms: $ \dfrac{1}{5} \div - \dfrac{9}{5} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{9}{5}$ is $- \dfrac{5}{9}$ Therefore: $ \dfrac{1}{5} \div - \dfrac{9}{5} = \dfrac{1}{5} \times - \dfrac{5}{9} $ $ \phantom{ \dfrac{1}{5} \times - \dfrac{5}{9}} = \dfrac{1 \times -5}{5 \times 9} $ $ \phantom{ \dfrac{1}{5} \times - \dfrac{5}{9}} = \dfrac{-5}{45} $ The numerator and denominator have a common divisor of $5$, so we can simplify: $ \dfrac{-5}{45} = \dfrac{-5 \div 5}{45 \div 5} = -\dfrac{1}{9} $